A many‐body version of the symmetry‐adapted perturbation theory is developed for a direct calculation of intermolecular potentials as a sum of the electrostatic, exchange, induction, and dispersion contributions. Since no multipole expansion is used, the obtained interaction energy components are properly dampened at short distance by the charge‐overlap (penetration) effects. The influence of the intramonomer correlation is accounted for by the perturbation expansion in terms of the Mo/ller–Plesset type fluctuation potentials WA and WB for the individual molecules. For the electrostatic and for the dispersion energy, the terms of the zeroth, first, and second order in WA+WB are considered. In this way, the leading three‐particle correlation contribution to the dispersion energy is taken into account. As a test of our method, we have performed calculations of the interaction energy for the water and hydrogen fluoride dimers. Both the geometry and the basis set dependence of the interaction energy component...

Many‐body symmetry‐adapted perturbation theory of intermolecular interactions. H2O and HF dimers

A perturbational method is described for calculating the interaction energy of two molecules in the region where the overlap between their wave-functions is significant. By working directly with a basis of determinants constructed from the SCF orbitals of the separated molecules, without orthogonalization, it is possible to avoid many of the disadvantages of other methods.

An intermolecular perturbation theory for the region of moderate overlap

A unified model, embodying the "pillow" effect and the induced density of interface states (IDIS) model, is presented for describing the level alignment at a metal/organic interface. The pillow effect, which originates from the orthogonalization of the metal and organic wave functions, is calculated using a many-body linear combination of atomic orbitals Hamiltonian, whereby electron long-range interactions are obtained using an expansion in the metal/organic wave function overlap, while the electronic charge of both materials remains unchanged. This approach yields the pillow dipole and represents the first effect induced by the metal/organic interaction, resulting in a reduction of the metal work function. In a second step, we consider how charge is transferred between the metal and the organic material by means of the IDIS model: Charge transfer is determined by the relative position of the metal work function (corrected by the pillow effect) and the organic charge neutrality level, as well as by an interface parameter S, which measures how this potential difference is screened. In our approach, we show that the combined IDIS-pillow effects can be described in terms of the original IDIS alignment corrected by a screened pillow dipole. For the organic materials considered in this paper, we see that the IDIS dipole already represents most of the realignment induced at the metal/organic interface. We therefore conclude that the pillow effect yields minor corrections to the IDIS model.

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Energy level alignment at metal/organic semiconductor interfaces: “Pillow” effect, induced density of interface states, and charge neutrality level

In the calculation of the interaction energy of two atoms, it is particularly convenient to take the zero order Hamiltonian H(0) to be the sum of the atomic Hamiltonians. Then H(0) does not reflect the full permutational symmetry of the exact Hamiltonian H. Many different perturbation expansions with such a ``nonsymmetric'' H(0) have been proposed. In this paper, these expansions are reviewed and classified within a very general perturbation framework. Also, a new ``optimized'' method is proposed which, by virtue of the Rayleigh‐Ritz variational principle, is guaranteed to give better results than any of the previously suggested methods. For simplicity the analysis is restricted to the case that the spin‐free zero order function φ(0) and the spin‐free exact wavefunction ψ are both nondegenerate. As an example, the construction of the first order wavefunction in each method is discussed in detail for the simple case of a single symmetry operation.

Perturbation theories for the calculation of molecular interaction energies. I. General formalism

The interaction between graphene layers is analyzed using a local orbital occupancy approach and second-order perturbation theory. This perturbation theory yields the van der Waals forces which are calculated, within the local orbital approach, using an atom-atom interaction approximation and the local density of states of the graphene layers. Weak chemical interactions (one electron, Hartree, exchange) are calculated using an expansion in the interlayer orbital overlap. We find that the one-electron repulsion due to orthogonalization effects is much larger than the Hartree and exchange contributions. The sum of these contributions yields a net repulsive short-range energy that counteracts the attractive long-range van der Waals interaction. Our analysis of the van der Waals interaction highlights the importance of the $2s\ensuremath{\rightarrow}3d$ atomic dipole transitions, which are responsible for more than half of the total van der Waals energy between two graphene layers. We obtain an interlayer equilibrium distance of $3.1\char21{}3.2\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, with a binding energy of $60\char21{}72\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, in reasonable agreement with the experimental evidence for graphite.

Weak chemical interaction and van der waals forces between graphene layers : A combined density functional and intermolecular perturbation theory approach

In order to treat the interaction energy of two molecules a standard Rayleigh-Schrodinger perturbation theory is developed. The Hartree–Fock functions of the separated molecules are used as one particle basis functions, the initial set of states being truncated and non-orthogonal. The non-orthogonality is included into the Hamiltonian by orthogonalization of the basis set. The unperturbed Hamiltonian is chosen so that it possesses the correct symmetry properties with respect to the electron permutations between different molecules. The procedure of this kind automatically results in the appearance of charge transfer states.



A graphical technique is elaborated which is a modified version of the Feynman–Goldstone technique and provides a convenient representation of the interaction energy contributions of any order. As an example the first- and the second-order diagrams are considered.



A correct expression for the dispersion energy is obtained which differs by a factor from that of the theory using a nonsymmetrical zero approximation.

M. V. Basilevsky

Papers

Intermolecular interactions in the region of small overlap